Absence of evidence and evidence of absence

It has been a while since my last blog post (yes, I love euphemisms). I have not been writing for the simple reason that I ran out of things to say, a fate that I am told few, very few amateur bloggers escape. So, what am I doing here now?

Well, I have been engaged lately in the same conversation with different friends and acquaintances, and I felt that I needed to collect my thoughts and write down a few basic points. That is when I remembered that I do have a blog, which allows one to get feedback (assuming anyone out there still reads this).

So, it all starts with a phrase that I hear often, in various contexts, mostly (but not exclusively) when discussing the supernatural, broadly construed. When its proponents, or believers, hear me express my scepticism toward it, motivated of the lack of verifiable, convincing, robust empirical evidence, they often state, as if it were a truism:

“Absence of evidence is no evidence of absence”

It is a popular line, as I have recently discovered. It seems to have some strange instant appeal. It might just be its catchiness, or maybe it does superficially sound plausible. After all, it is used also by prominent debaters and opinion makers. The problem is, it is a fallacious statement.
Actually, let me rephrase it as follows:It is utter, unmitigated nonsense. And, it is almost always used disingenuously by individuals who would dismiss it without giving it a second thought in any other context, but have no qualms making it part of the special pleading for their favourite superstition.

What could possibly constitute evidence of absence, other than absence of evidence?
It may not necessarily be definitive evidence of absence [0], or “proof” thereof (whatever meaning can be ascribed to a word such as “proof” outside the confines of mathematics). Granted, one should always exercise caution, abide by rigorous procedures and carefully assess whether a bona fide effort was made to collect whatever cogent evidence is needed to support a specific hypothesis or claim. But the notion that lack of evidence should not be seen as rather pointing to the invalidation than to the validation of a claim, seems truly bizarre. It is hopelessly at odds with a commonly accepted part of society’s modus operandi, one with major implications in all different aspects of daily life — even legal.
Inability to gather supporting evidence — of the believable kind, that is one that would be given credence in a professional setting, in a science laboratory or in a court of law, eventually must and does lead reasonable individuals to conclude that a claim simply does not hold water, no matter how appealing it is. When asked an opinion about it, said individuals will normally use their favourite vernacular expression to signify its almost certain falsehood.

And the vast majority of us are reasonable most of the time (thankfully). Only a minority go around saying things such as, “the jury is still out on alien abduction”, “can we really exclude that unicorns exist?”, or “it has not really been proven that astrology has no foundation”.
Indeed, we are all required on a daily basis to exercise healthy scepticism toward the numerous, preposterous claims with which we are confronted (typically referred to as quackery) — from dubious alternative remedies for ailments for which conventional medicine still has no solution, to dodgy investment schemes that will quadruple our fortune in a month, to puzzling devices capable of generating unlimited amounts of energy at no cost. It is precisely the absence of any credible, robust, objective evidence in support of these contentions, that makes most of us dismiss them offhand as nothing but scams (and usually shake our head in disbelief at the few unfortunate ones who fall for them).
Now, is it strictly “impossible” that any of these claims may actually be true?
Well, no, and that is precisely the point. A lot of things may be possible. We know that the world is a surprising place, and that occasionally scenarios deemed exceedingly unlikely do actually turn out to be true… bust most of them, most of the time, do not, whence the motto “if it sounds to good to be true…”.
That is why the burden of proof, namely providing supporting evidence, always fall on those making the positive claim (i.e., that something exists or happens), not on those who doubt it. It is also why, for instance, any reasonable and fair judiciary system is based on the “innocent until proven guilty” principle. It is because affirming something does not make it true. The thought is actually pretty scary of where we could end up, as a society, were the burden of proof tenet turned upside down.

Scientific evidence
Nowhere as in the realm of scientific research does the absurdity of the mantra “absence of evidence is no evidence of absence” hit one’s face. For, not only is absence of evidence universally regarded as just that, namely evidence of absence — it is the only acceptable, or even conceivable “evidence of absence”.
Consistent, systematic failure to observe in controlled conditions a phenomenon or outcome predicted by a theory is ultimately seen as the demonstration that the phenomenon does not take place — at least not as predicted, and that the underlying theory is flawed. This is why, for example, you will never hear a (sane) physicist say something like “Although aether has never been observed, that by itself is no sufficient reason to rule out its existence” — they will all say that aether does not exist [1].
And it is not that way just in physics; among the countless examples that I could mention, absence of evidence is how medical researchers establish the inefficacy of proposed drugs or treatments, or how sceptics of global warming try to undermine the scientific case for it, as they endeavour to dispute and/or nullify the evidence put forth by their opponents.

In summary…
Absence of evidence is evidence of absence. Always. Pretty much no matter how you cut it [2]. Those who state that “absence of evidence is no evidence of absence” have made an act of faith into something for which there is no evidence, and would simply reject a priori any argument undermining their unsubstantiated belief. Don’t get me wrong, everyone is entitled to believe what they like, but please, let’s keep the discussion rational.

Addendum
I have found here a Bayesian argument to the effect that absence of evidence is evidence of absence very similar (actually identical) to mine. I am sure it was published before mine, but I did derive it independently (after all, it is rather trivial).

Notes

[0] Naturally, in this post I am referring to evidence that 1) is relevant to supporting the claim and 2) has been and is being actively sought by any possible means, and if found would be promptly disseminated. Ignorance, suppression or temporary unavailability of evidence are obviously not the same as absence thereof.
It is certainly possible, and routinely happens, that what was once regarded as unlikely, or even impossible (e,g,. the expansion of the universe at an accelerating rate), suddenly acquires plausibility in light of new evidence, once unattainable, yielded by technological advances (the Hubble telescope). There also exist, of course, situations in which evidence may be intrinsically unobtainable, due to unalterable physical limitations. For example, we may never be able to answer, through evidence, the question of whether there is life elsewhere in this universe, even though its sheer vastness renders astronomically small the odds that it only exist on planet Earth.

[1] And no, the reason is not that, as a concept, aether was rendered superfluous by Einstein’s theory of special relativity, but because landmark experiments such as the Michelson-Morley or Fizeau simply failed to detect its effect in conditions where it should have been detectable, according to the theory.

[2] If you spend some time on the internet (e.g., YouTube), you will see that there are a lot of individuals who have tried to prove that absence of evidence is/is not evidence of absence using Bayesian inference.
It is not central to what I discuss in this post, but, just for the fun of it I have worked out my personal proof — here it is. I am using standard Bayesian notation. I not an expert and comments are welcome (yes, this is the one and only reason I wrote this boring post).

We begin with a definition:
Given a hypothesis A, proposition B is evidence for A if
P(A|B) > P(A), (1)
i.e., if the probability that A be true given that B is true, is greater than the prior probability that A be true (i.e., without the added knowledge that B is true).
It follows from (1) that
P(A|~B) < P(A), (2)
where ~B stands for “B not being true”, or, evidence B being absent. In other words, if B being true renders A more likely to be true, then B being untrue has the opposite effect, i.e., it weakens the likelihood that A itself is true.Proof:
It is P(A,B)+P(A,~B) = P(A) (3)
Using Bayes’ theorem, as well as P(B) + P(~B) = 1, we can rewrite (3) as
P(A|B) P(B) + P(A|~B) P(~B) = P(A) P(B) + P(A) P(~B), which can be rearranged as
[P(A|B) – P(A)] P(B) = [P(A) – P(A|~B)] P(~B) (4)

Since 0 < P(B), P(~B) < 1, and because by (1) [P(A|B) – P(A)] > 0, it follows that necessarily

[P(A) – P(A|~B)] > 0, or P(A|~B) < P(A), q.e.d.

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